There are a number of potential voltage instability problems which can arise within an electrical power system. Some of these instability problems occur in distribution systems used for distributing electrical power to utility customers. Many of the sources of these distribution system voltage stability problems have existed for years, and their causes and solutions are well known in the art.
Other problems occur in transmission systems, which are used for transporting bulk power from generation stations to load centers. These stability problems result from such causes as facility outages, clearing of short circuit faults, and increases in load power or inter-area power transfer in a transmission network. Many of these transmission system voltage instability problems have been encountered only in recent years. These instability problems have occurred as a result of recent trends toward: locating generation stations distantly from load centers which limits the effectiveness of their voltage controls, requiring utilities allow power shipment across their transmission system by independent power producers or other utilities, and deterring construction of needed transmission networks, to name a few.
A slow-spreading, uncontrollable decline in voltage, known as voltage collapse, is a specific type of transmission system voltage instability. Voltage collapse results when generators reach their field current limits which causes a disabling of their excitation voltage control systems. Voltage collapse has recently caused major blackouts in a number of different countries around the world.
In order to reduce the possibility of voltage collapse in a power system, and more generally, improve the stability of the power system, system planning is performed by many utility companies. First, a mathematical model representative of the basic elements of the power system, and their interconnection, is constructed. These basic elements include generating stations, transformers, transmission lines, and sources of reactive reserves such as synchronous voltage condensers and capacitor banks. Next, various computational techniques for analyzing system stability are performed using a suitably programmed computer. Based on this analysis, proposed enhancements are formulated in an ad-hoc manner for improving voltage stability security. The mathematical model can be updated based upon these proposed enhancements so that the resulting system stability security can be analyzed. Enhancements which attain predetermined design objectives are then physically implemented in the actual power system. The process of system planning is continual in that it must be regularly performed in light of changing circumstances.
In mathematical terms, voltage collapse occurs when equilibrium equations associated with the mathematical model of the transmission system do not have unique local solutions. This results either when a local solution does not exist or when multiple solutions exist. The point at which the equilibrium equations no longer have a solution or a unique solution is often associated with some physical or control capability limit of the power system.
Current methods for assessing proximity to classic voltage instability are based on some measure of how close a load flow Jacobian is to a singularity condition, since a singular load flow Jacobian implies that there is not a unique solution. These proximity measures include: (i) the smallest eigenvalue approaching zero, (ii) the minimum singular value, (iii) various sensitivity matrices, (iv) the reactive power flow-voltage level (Q-V) curve margin, (v) the real power flow-voltage level (P-V) curve margin, and (vi) eigenvalue approximation measures of load flow Jacobian singularity.
The eigenvalue and minimum singular value methods are disadvantageous in their lacking an indication of the actual locations and causes of voltage instability. Moreover, these methods have been known to produce misleading results with respect to causes of voltage instability as well as the locations and types of enhancements necessary to improve voltage stability security. Furthermore, the computational requirements for the eigenvalue and minimum singular value methods are relatively high. The sensitivity matrix methods have many of the same difficulties as the eigenvalue and singular value methods resulting from being linear incremental measures for a highly-nonlinear discontinuous process.
Regardless of the method employed for assessing proximity to classic voltage instability, existing methods employed by many utility companies assume that there is only one voltage instability problem. Further, it is assumed that one distributed reactive power loading pattern test detects the one voltage instability problem.
It is known that a voltage control area may be defined as an electrically isolated bus group in a power system. Reactive reserves in each voltage control area may be distributed via secondary voltage control so that no generator or station would exhaust reserves before all the other generators in the voltage control area. Although this secondary voltage control is effective in preventing classic voltage instability, previously defined voltage control areas are no longer valid whenever the originally existing transmission grid is enhanced so that bus groups are no longer as isolated. A further disadvantage of this approach is that the reactive reserves for controlling each voltage control area are limited to be within the voltage control area.
Methods are also known which employ a voltage zone defined as a group of one or more tightly-coupled generator P-V buses together with the union of the sets of load buses they mutually support. In such methods, amount of reactive power supply to maintain an acceptable voltage level is controlled. A disadvantage of this approach, however, is that characterizing a voltage stability margin in terms of voltage does not protect against classic voltage collapse.
Current engineering methods of locating potential voltage instability problems includes simulating all single line outage contingencies, and identifying those that do not solve as causing voltage instability. However, the lack of a solution is not a guarantee of voltage instability; a lack of a solution can occur because: the load flow Newton-Raphson-based algorithms are not guaranteed to converge from any particular starting solution, but converge only when the starting point is sufficiently close to the solution; the load flow convergence is not guaranteed even when the system is close to a solution if the solution is close to a bifurcation; round-off error affects the load flow convergence; and discontinuous changes due to switching of shunt elements, or outages of generators or lines can have a dramatic effect on whether the load flow algorithm will converge to a solution. The converged solutions for all single outages only indicates that there are no bifurcations. In order to attempt to prove that the absence of a converged solution is caused by voltage instability, substantial manpower and computer processing time are required. In one such method, the absence of a converged solution is determined to be due to voltage collapse if one can add a fictitious generator with infinite reactive supply at some bus to obtain a converged load flow solution. This method is not foolproof, and furthermore, does not indicate the causes of voltage instability nor indicate where it occurs.
However, current methods are incapable of identifying all of the many different voltage stability problems that can occur in a transmission system. A very routine operating change or supposedly insignificant contingency in a remote region of the system, followed by another contingency, can cause voltage instability. Furthermore, voltage instability may occur in many different sub-regions of the system. Current methods lack diagnostic procedures for identifying causes of specific voltage stability problems, as well as systematic and intelligent enhancement procedures for preventing voltage instability problems.